A structural model of a micropolar continuum
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Abstract In their crystal lattice theory, Born-Von Karman have shown that the long wave approximation to their model yields the equations of the classical theory of elasticity. The Born-Von Karman model assumed that the interaction between the particles can be characterized by a simple spring which allows extensions only. Also, in their model, the dimensions of the particles are shrunk to zero thus resulting in non-orientable mathematical points. In this paper, a two dimensional model composed of orientable points, joined by extensible and flexible rods is presented in order to explain the foundations of the Cosserat [1] or the micropolar continuum [2]. As the long wave approximation from this model, one gets the coupled displacement and microration equations of the micropolar medium, similar to those given by Eringen and Suhubi[2, 3] and by Mindlin[4, 5].
[1] E. Cosserat,et al. Théorie des Corps déformables , 1909, Nature.
[2] R. D. Mindlin. Stress functions for a Cosserat continuum , 1965 .
[3] A. Cemal Eringen,et al. Nonlinear theory of micro-elastic solids—II☆ , 1964 .
[4] R. D. Mindlin. Micro-structure in linear elasticity , 1964 .
[5] A. Cemal Eringen,et al. NONLINEAR THEORY OF SIMPLE MICRO-ELASTIC SOLIDS-I , 1964 .